Question

Kyle drops a ball from a height of 15 feet above the ground. The function h = −16t^2 + 15 gives the height h of the ball (in feet) after t seconds. Graph the function. Then determine the approximate time the ball hits the ground.

Answer 1

To graph the function h = -16t^2 + 15, substitute different values of t into the equation. The positive solution using the quadratic formula represents the time when the ball hits the ground.

Step-by-step explanation:

To graph the function h = -16t^2 + 15, we can plot points by substituting different values of t into the equation and calculating the corresponding values of h. For example, when t = 0, we have h = -16(0)^2 + 15 = 15. So, the first point on the graph is (0, 15). Similarly, when t = 1, we have h = -16(1)^2 + 15 = -1. Hence, the second point on the graph is (1, -1). We can continue this process to plot additional points and then connect them to form the graph of the function.

The ball hits the ground when h = 0. So, we can set -16t^2 + 15 = 0 and solve for t. This is a quadratic equation, and we can use the quadratic formula to find the solutions. In this case, the positive solution represents the time when the ball hits the ground. Therefore, we can approximate the time the ball hits the ground by finding the positive solution using the quadratic formula.

Let’s calculate: -16t^2 + 15 = 0 => t^2 = 15/16 => t = ±√(15/16).